Recursive Design of High Girth (2,k) LDPC Codes from (k,k) LDPC Codes

An approach to construct column-weight-2 LDPC codes with high girth is presented. The approach derives a column-weight-2 LDPC code from the Tanner graph of a (k,k) QC-LDPC code. By the construction, the new LDPC codes double in girth. To construct the (k,k) QC-LDPC codes with desired girth, a search algorithm is proposed in this paper. The approach generates an example of a (2,3) LDPC code with a girth of 36, which is larger than the column-weight-2 LDPC codes constructed by the previously methods.

[1]  David Declercq,et al.  Design of cages with a randomized progressive edge-growth algorithm , 2008, IEEE Communications Letters.

[2]  B. V. K. Vijaya Kumar,et al.  Low complexity LDPC codes for partial response channels , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[3]  Marc P. C. Fossorier,et al.  Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices , 2004, IEEE Trans. Inf. Theory.

[4]  Jose M. F. Moura,et al.  Large-girth LDPC codes based on graphical models , 2003, 2003 4th IEEE Workshop on Signal Processing Advances in Wireless Communications - SPAWC 2003 (IEEE Cat. No.03EX689).

[5]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[6]  Sunghwan Kim,et al.  Quasi-Cyclic Low-Density Parity-Check Codes With Girth Larger Than $12$ , 2007, IEEE Transactions on Information Theory.

[7]  Shu Lin,et al.  Low-density parity-check codes based on finite geometries: A rediscovery and new results , 2001, IEEE Trans. Inf. Theory.

[8]  Mehdi Gholami,et al.  Geometrically-structured maximum-girth LDPC block and convolutional codes , 2009, IEEE Journal on Selected Areas in Communications.